## Exponential Period of Neuronal Recurrence Automata with Excitatory Memory

**René Ndoundam***Electronic mail address: ndoundam@uycdc.uninet.cm.*

**Maurice Tchuente***Electronic mail address: tchuente@camnet.cm.**Department of Computer Science,**Faculty of Science, University of Yaounde I,**P.O. Box 812 Yaounde, Cameroon*

#### Abstract

The sequences generated by a neuronal recurrence equation with memory of the form $x\left(n\right)=1\left[{\sum}_{i=1}^{h}{a}_{i}x\left(n-i\right)-\theta \right]$, where *h* is the size of the memory, are studied. It is shown that in the case where all the parameters ${\left({a}_{i}\right)}_{1\le i\le h}$ are positive reals, there exists a neuronal recurrence equation of memory length *h* that generates a sequence of period $\Omega \left({e}^{\sqrt[3]{{h\left(\mathrm{ln}\left(h\right)\right)}^{2}}}\right)$. This result shows that in the case where all the weighting coefficients are positive reals, the neuronal recurrence equation exhibits a complex behavior.